Our study of vector boson (V ) production in conjunction with a D*(2010)+ meson is presented. Using a data sample correponding to 9.7 fb-1 p of proton-antiproton collisions at center-of-mass energy √s = 1:96 TeV produced by the Fermilab Tevatron, we reconstruct V +D*+ samples with the CDF II detector. The D*+ is fully reconstructed in the D*(2010)+ → D0(→ K- π+)π+ decay mode. This technique is sensitive to the associated production of vector boson plus charm or bottom mesons. We measure the ratio of production cross sections σ(W +D*)/ σ(W) = [1.75±0.13(stat)±0:09(syst)]% and σ(Z +D*)/ σ(Z) = [1:5±0:4(stat)_0:2(syst)]%. Event properties are utilized to determine the fraction of V +D*(2010)+ events originating from different production processes. Our results are in agreement with the predictions obtained with the pythia program, limiting possible contribution from non-standard-model physics processes.